Just a thought, the Bureau of Justice Statistics suggests FBI crime statistics are an extreme underestimation: bjs.gov/index.cfm?ty=tp&tid=37. That's because not all police departments report hate crimes.
– wirefireFeb 8 '17 at 21:00

@wirefire you're definitely on the right track - one needs to take lots of care when analysing these issues, as the typical biases one sees in studies are amplified for controversial/personal issues.
– Anthony JosephFeb 9 '17 at 1:09

What about segregation? I wouldn't claim that it directly assumes racism, but it's one potential metric. You could use the USA Today diversity index to measure segregation on a town, neighborhood, or even block level, if you use the 10-year Census data.

That's a very good point. I know there are population by ethnicity statistics available down to the block group level from the American Community Survey. But if there is anything related on the block level that would be very interesting. Do you have a source for that?
– eigenvectorFeb 8 '17 at 23:01

I'm not sure I follow you. In my experience, the ACS goes down to the town level, although some towns will have a high margin of error, particularly when dealing with small sub-populations like ethnic groups. The 2010 Census data is available by "tract," which is typically smaller than town, or by block. IPUMS would allow you to fetch historical variables in some cases, although the variables for Hispanic ethnicity, among other things, has changed over the years.
– wirefireFeb 9 '17 at 16:16

I don't know about towns but I was under the impression that the ACS provides population estimates down to the block level and economic and social variables down to the block group level (which is one level less detailed but in turn more detailed than the tract-level). Also, I always thought that there was no data source (whether Census, ACS etc.) that provides any economic or social outcomes at the block level but if there does exist such information from ACS I'd be curious to know.
– eigenvectorFeb 9 '17 at 17:46

In general, this is difficult because (I assume) there exist no indices or direct measures of racism at the county-level.

Likely as not, you will need to find a variable that xenophobic tendencies in a society and therefore provides an indirect measure of racism. One idea that comes to my mind is that you could look at top-level professionals such as CEOs, CFOs, member of company boards, high-level government employees etc. and see how the share of ethnic minorities in these positions varies over time and from county to county. This is no direct measure of racism but rather of how well ethnic minorities do in a particular society which might very well be related. The advantage is that such data is often publicly available.

Edit: additional information.

I just came across this working paper by Economists Bonick and Farfan-Vallespin from December 2016 which deals with the causes and consequences of racism. In order to measure racism, the authors follow an interesting strategy:

We use a novel way for measuring racism extracted from the World Value
Survey (my emphasis). The variable is derived from the question, ”On this list are
various groups of people. Could you please mention any that you would
not like to have as neighbors?”. The groups in the list include
criminals, people from other religions, homosexuals, terrorists, and
people from another race, among many others. We are as far as we
know the first ones to identify a way of measuring racism and to
attempt to address these questions at the macroeconomic level.

This is fairly straightforward and might help you if you are also interested in racism on an international level. The data from the World Value Survey can be downloaded here.

^ In addition to great responses above, may I recommend that operationalizing racism matters a lot for measuring it. Personally I follow People's Institute for Survival and Beyond's definition - something like: power+prejudice, within an individual (internalized supremacy / inferiority), between individuals (interpersonal bias / prejudice, explicit or implicit, acted on or latent), institutional (laws, policies, etc., formal and informal) and cultural.

So racism is multi-level power plus prejudice at all those levels.

One of my topics of research is racial disparities in police traffic stops, which I could talk more about, but is a specific form of institutional/cultural race discrimination pressure often built on racist structures and attitudes. Some also look at measures like income inequality by race, or power inequalities, like voting turn out or board / governnment representation. Some recent data scientists have looked at explicitly racist google searches (available through google trends work), and mapped that. Others have looked at things like dating websites and questions about interracial dating.